Difference between revisions of "Upper attic"

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Line 34: Line 34:
 
* [[Ramsey]] cardinal
 
* [[Ramsey]] cardinal
 
* [[virtually Ramsey]] cardinal
 
* [[virtually Ramsey]] cardinal
*[[$\alpha$-iterable]] cardinal
 
 
* [[Rowbottom]] cardinal
 
* [[Rowbottom]] cardinal
 
* [[Jonsson | Jónsson]] cardinal
 
* [[Jonsson | Jónsson]] cardinal
Line 40: Line 39:
 
* [[zero sharp | $0^\sharp$]]
 
* [[zero sharp | $0^\sharp$]]
 
* [[Erdos | Erdős]] cardinal, and the [[Erdos | $\alpha$-Erdős]] hierarchy for countable $\alpha$
 
* [[Erdos | Erdős]] cardinal, and the [[Erdos | $\alpha$-Erdős]] hierarchy for countable $\alpha$
 +
*[[$\alpha$-iterable| $1$-iterable]] cardinal, and the [[$\alpha$-iterable]] cardinals hierarchy for $1\leq \alpha\leq \omega_1$
 
* [[remarkable]] cardinal
 
* [[remarkable]] cardinal
 
* [[completely ineffable]] cardinal
 
* [[completely ineffable]] cardinal
* [[ineffable]] cardinal
+
* [[ineffable]] cardinal, and the $n$-ineffable cardinals hierarchy
 
* [[weakly ineffable]] cardinal
 
* [[weakly ineffable]] cardinal
 
* [[subtle]] cardinal
 
* [[subtle]] cardinal

Revision as of 14:29, 20 January 2012

Cape Pogue Lighthouse photo by Timothy Valentine

Welcome to the upper attic, the transfinite realm of large cardinals, the higher infinite, carrying us upward from the merely inaccessible and indescribable to the subtle and endlessly extendible concepts beyond, towards the calamity of inconsistency.